If you go with the "standard" idiomatic usage "Opportunity at her fingertips" this issue just doesn't arise.
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FumbleFingersAug 8 '12 at 17:50

I suppose my question is better phrased as: Is there a scenario in which "at the tip of her fingers" is correct?
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bibsAug 8 '12 at 17:54

I suppose it could be considered "valid" by some (perhaps many) speakers - but why not just use at her fingertips, which would be considered "normal" by practically everyone?
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FumbleFingersAug 8 '12 at 17:56

This is a specific issue I'm debating with someone. I'm looking for the answer to this question not a better alternative.
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bibsAug 8 '12 at 18:04

I don't understand the point of debating the hypothetical correctness or otherwise of a form people don't normally use. (Unless it's just to establish that the reason we don't use either of your alternatives is because we can't agree which! :)
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FumbleFingersAug 8 '12 at 21:10

When you say "the tips of my fingers", you are referring to the individual tips of each finger. A possible usage would be "I felt a tingling in the tips of my fingers".

However, when you're talking about a more metaphorical something that's just within reach, you would use "the tip of my fingers", since you're referring to all your fingers - your figurative "reach" - as one unit.

For me, the "standard" metaphoric usage is "at his fingertips". I'm not going to try and count the relevant hits in that link - but it's at least tens, if not hundreds of thousands.

Having said all that, regarding OP's specific usage, I think the "correct" version would be "at the tip of her fingers", since the intended sense is of a singular metaphoric reach, ability to access easily.

But if, say, an investigative journalist were talking to his editor, he might more correctly say "I have several reliable sources at the tips of my fingers", since in that case he'd be talking about easily reaching different people in different places.

Why would the "singular metaphoric reach" cause "tips" to become "tip," if fingers is plural? Doesn't "tips" still refer to fingers?
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bibsAug 8 '12 at 18:01

@bibs: Just because we're only interested in one particular tip - the "collective" one of the outstretched fingers reaching towards the thing being talked about. It's one "reach", not many.
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FumbleFingersAug 8 '12 at 21:07

As I have always done, I will use my own language to help in this answer. Supposedly, when you say "cars", you mean more than one. When you talk about "the motor of the cars", you're referring to a unique model of motor that works in every car, so the motor is repeated after every car, being the car different, but not the motor.

After that, you could say "cars" and then talk about the "the motors of the cars" and you'll be referring to every motor of every car but never stating that they are the same. The previous sentence implies that the motor is the same for the cars.

In your case, the fingers have tips. But the fingers have everyone, a tip. And that's the clue. You may use both with the only difference that the singular form is a generic or general to denominate repeating objects that are almost the same, and the plural, that reveals that being repeating objects almost the same doesn't make them equals.

Sometimes, when you're being so specific, it just has real importance when you're using it (the sentence) in a phrase that requires a clear definition about the question of being many or just one part that repeat in many others. If that is not the case (an expression for example) I don't think you need so much clarity.

EDIT:

Giving a good look at the other answers I realized they are right about the metaphorical use of tip v/s tips. I think that's also a good point.